DKK
97.5%
The figure shows daily Value-at-risk & Expected Shortfall risk predictions together with daily Profit/Loss observations. The “red” dots highlights the Value-at-Risk-events where the Profit/Loss is worse (more negetive) than predicted by Value-at-Risk.
| Backtest Results | |||||
|---|---|---|---|---|---|
| Value-at-Risk & Expected Shortfall | |||||
| Year | #VaR-Events | #Obs | ES-Test-Stat | Test for Accuracy (p-value) | |
| Value-at-Risk1 | Expected-Shortfall1 | ||||
| By year | |||||
| 2018 | 5 | 260 | 0.1341 | p-value >= 0.1 | p-value >= 0.1 |
| 2019 | 5 | 261 | 0.2167 | p-value >= 0.1 | p-value >= 0.1 |
| 2020 | 7 | 262 | -0.1552 | p-value >= 0.1 | p-value >= 0.1 |
| 2021 | 6 | 261 | 0.0846 | p-value >= 0.1 | p-value >= 0.1 |
| 2022 | 6 | 193 | -0.1050 | p-value >= 0.1 | p-value >= 0.1 |
| All years | |||||
| 29 | 1,237 | 0.0425 | p-value >= 0.1 | p-value >= 0.1 | |
| Reference: Carlo Acerbi & Balazs Szekely (2014) BACKTESTING EXPECTED SHORTFALL, MSCI. The unconditional test statistic (test 2) are used here | |||||
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1
The p-value tells you how likely it is to observe a worse outcome under the null hypothesis of an accurate model.
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The summary of the backtest is created based on the daily input-values for Profit/Loss, Value-at-Risk and Expected-Shortfall. The p-value can be interpretated as a likelihood of observing an even worse outcome than observed (i.e. more frequent loss-events for Value-at-Risk and more severe losses for Expected-Shortfall) under the assumption that the model is accurate (the null hypothesis). In case where the p-value is low this is used as evidence against the hypothesis and hence conclude that the model show signs of not being accurate.
| Colour Schema |
|---|
| p-value |
| Interpretation |
| p-value >= 0.1 |
| p-value < 0.1 |
| p-value < 0.05 |
| p-value < 0.02 |
| p-value < 0.01 |
| p-value < 0.005 |
| p-value < 0.001 |
| Reference: Basel Committee on Banking Supervision (2019) Minimum capital requirements for market risk, 'MAR99 Guidance on use of the internal models approach', table 2 (p. 128). The colour schema is an ENVISIONRISK adoptation of the chosen cutoff values in the BIS paper. |
The interpretation of ‘p-value < 10%’ is that the p-value is higher than 5% but lower than 10%. The same rationale for the rest of the p-values. We dont calculate an exact p-value, but only calculte it for certain cutoff values.